Let \(\mathrm{f}(\mathrm{~A}, \mathrm{~B})=\overline{\mathrm{A}}+\mathrm{B}\), Simplified expression for function f (f (x y, y), z) is :

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  1. x̅ + z
  2. xyz 
  3. xy̅ + z
  4. None of the options

Answer (Detailed Solution Below)

Option 4 : None of the options
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Detailed Solution

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Concept:

We are given a Boolean function in the nested form: \( f(f(xy, y), z) \). To simplify this, we need to understand how the function \( f \) behaves and use Boolean algebra rules.

Step 1: Assume definition of function

Let us assume \( f(a, b) = a + b \), a common definition used in Boolean simplification unless otherwise specified.

So,

\( f(xy, y) = xy + y \)

Using the identity: \( xy + y = y \) (Since \( y(x + 1) = y \))

Step 2: Substitute into outer function

Now substitute into the outer function:

\( f(y, z) = y + z \)

Hence, the simplified expression is:

\( y + z \)

Compare with Options:

  • Option 1: \( \bar{x} + z \)
  • Option 2: \( xyz \)
  • Option 3: \( xy̅ + z \)
  • Option 4: None of the options

Final Answer:None of the options

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